Summary: The statistics of intermittency maps
dynamical modelling of networks
, M. Barenco
, R.J. Mondragon
, M. Woolf
July 12, 2004
The paper is split into two parts. The first indicates the form of the proof of an autocorrelation result for
a double intermittency map of the interval. The specific map considered is a piece-linear map of the interval.
The map is then used in the second part of the paper for modelling sources of long-range dependent traffic in a
network. The main ingredients are the production of packets of data at the nodes of a network and the transfer
of the data around the network. The behaviour of packet lifetime and throughput is compared for both closed
and open loop models, and also long-range-dependent Poisson-like traffic sources.
In the early 1990's, Leland and coworkers  showed that packet traffic in computer networks exhibited long range
dependence when it was previously thought that data traffic packet rates, like voice traffic, would be memoryless.
This has major consequences as long-range-traffic is also bursty and poses major engineering challenges, at timescales
spanning several orders of magnitude.